I think the Battle off Samar is the easiest counter example to your thesis. American destroyers and air units took on a Japanese surface force that included all major surface types except carriers. The Americans were able to delay the Japanese force, but were mauled in the process. There were a number of battles in "Ironbottom Sound" that would also be illustrative.

AAA was a deterrent to an attacking air unit, but even with a large fleet one could not completely stop an incoming air attack. Put simply, while AAA could make an air attack more costly bombers were still a lethal threat to surface ships and their range and speed advantages over surface ships made them able to attack a purely surface force repeatedly before it could close to a distance at which it could counter-attack.

In addition to /u/Domini_canes post, Ill add that battleships were designed to counter all kinds of threats. Their main batteries were extremely powerful, and could cause major damage to a lightly armored ship like a destroyer. Further, battleships had secondary armaments which were specifically designed to destroy torpedo boats before they launched their torpedos. Then there is the problem of the the battleship's own escorts, which were again designed to attack destroyers and light ships while the battleships were free to concentrate against larger targets.

Then, even if the destroyers launched their torpedoes there was no guarantee that they would hit, World War Two torpedoes were unguided, or that they would destroy the target, heavy ships universally had large torpedo bulges which could be damaged and flooded without compromising the ship's overall integrity.

On top of the great answers ill add 2 more considerations.

1. Is range. DD's didnt have the range to go huge distances, so they would have had to have oilers with them, which would then slow them down. Where Fast Battleships and carriers could top off their escorts from their own tanks at remain at a higher speed.

2. Is the purpose of a navy. It isnt just to defeat other navies. It is to project power FROM the sea, now sea lane control and operational freedom is part of that but it isnt everything. For instance when bombarding enemy coastal positions or fortifications the light guns of a DD arent going to do much. Then you need the big 12/14/16 in guns of the battle line, or even better timely and local air support from the flat tops.

In WWII the two most valuable types of naval ships proved to be submarines and aircraft carriers, not destroyers.

For torpedo attacks, submarines were considerably more stealthy, survivable and deadly than destroyers. 55% of all Japanese ships sunk by US action in WWII were sunk by submarines.

Most of the rest were sunk by aircraft.

The main role of destroyers in WWII was to hunt and deter submarines, not to launch torpedoes at surface ships. (The original role of destroyers - pre WWI - was to launch torpedoes at surface ships, but they had largely abandoned this role during WWI let alone WWII.)

Submarines were much less vulnerable to air attack than destroyers.

By WWII destroyers primary role was anti-submarine defense. Their secondary role was anti-aircraft defense (in support of larger capital ships), their very minor tertiary role was to conduct torpedo attacks against surface ships.